When is it reasonable to demand the removal of an adrenal tumor?

Activity, Size. Any adrenal tumor that is producing excessive amounts of adrenal hormones requires treatment; this can be determined by a battery of blood and urine tests. If the tumor is "non-functioning" (as most are), removal is dependent upon size: those under 4cm can be watched; those over 6cm should be removed; for those "in the middle", it depends upon what it looks like by ct or MRI criteria.
Never. It is never reasonable to demand a surgical procedure. If you disagree with the recommendation that you have received, solicit other opinions. Regarding adrenal masses. Many are small and do not produce hormones. In most cases, they can be safely followed by ct.